Inserted: 12 oct 1999
Last Updated: 6 mar 2007
Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)
Volume: XXIX (2000)
In this note we consider a notion of rearrangement which extends to n dimensions the familar notion of increasing rearrangement for functions of one variable, and study the behaviour of some classes of integral functionals with respect to this operation. Among other applications, we obtain a simple direct proof of the existence and uniqueness of n-dimensional optimal profiles for transitions in a phase-separation model with a non-local interaction energy.
Keywords: increasing rearrangement, rearrangement inequalities